spc capability
Process capability in SPC measures a process's ability to produce output within specification limits — it quantifies how well the natural variation of the process fits within the required tolerance window. High capability means the process consistently produces results well within spec; low capability means the process frequently approaches or exceeds the limits.
Key Capability Metrics
- Cp (Process Capability Index):
C_p = (USL - LSL)/(6 sigma)
Compares the specification width to the process spread. Does not consider process centering — it measures potential capability if the process were perfectly centered.
- Cpk (Process Capability Index, Centered):
C_pk = min((USL - bar(X))/(3 sigma), (bar(X) - LSL)/(3 sigma))
Accounts for how close the process mean is to the nearer spec limit. Always ≤ Cp. Cpk = Cp only when the process is perfectly centered.
Interpreting Capability Values
| Cpk Value | Interpretation | PPM Defective |
|---|---|---|
| < 1.0 | Not capable — significant out-of-spec production | >2,700 |
| 1.0 | Barely capable — 3σ limits touch spec limits | 2,700 |
| 1.33 | Acceptable — standard industry minimum | 63 |
| 1.67 | Good — typical target for critical steps | 0.6 |
| 2.0 | Excellent — 6σ process | 0.002 |
Why Capability Matters in Semiconductors
- A CD process with Cpk < 1.33 produces too many out-of-spec features — directly causing yield loss.
- Critical steps (gate CD, overlay, film thickness for thin films) often require Cpk ≥ 1.67.
- Non-critical steps may accept Cpk ≥ 1.0, but improvement is expected.
- Cp vs. Cpk Gap: If Cp is high but Cpk is low, the process has adequate precision but is off-center — a simple target adjustment can improve Cpk.
Improving Process Capability
- Reduce σ: Tighten the process spread through equipment improvements, recipe optimization, or better raw materials. This improves both Cp and Cpk.
- Center the Process: Adjust the process mean to the midpoint of the specification range. This improves Cpk without changing Cp.
- Widen Specifications: If the specs are unnecessarily tight, relaxing them improves capability — but this requires design validation.
Process capability is the ultimate measure of process quality — it directly connects manufacturing variation to product specifications and defect rates.